{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BUI3LLQZPZRRWS4XT5KFJBHMCX","short_pith_number":"pith:BUI3LLQZ","canonical_record":{"source":{"id":"1505.07577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-28T07:50:28Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"eef1d879bd3fbc4f91a54d8c1e185ad3640913d5c16cc933af813433656aa77f","abstract_canon_sha256":"10d48601e409a59dd780e09a0987bd898b96a12c917fe3b2f6e559e5db092a51"},"schema_version":"1.0"},"canonical_sha256":"0d11b5ae197e631b4b979f545484ec15d7dd6dbf5b9998cf93c398834aa640ec","source":{"kind":"arxiv","id":"1505.07577","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.07577","created_at":"2026-05-18T00:41:28Z"},{"alias_kind":"arxiv_version","alias_value":"1505.07577v1","created_at":"2026-05-18T00:41:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07577","created_at":"2026-05-18T00:41:28Z"},{"alias_kind":"pith_short_12","alias_value":"BUI3LLQZPZRR","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BUI3LLQZPZRRWS4X","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BUI3LLQZ","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BUI3LLQZPZRRWS4XT5KFJBHMCX","target":"record","payload":{"canonical_record":{"source":{"id":"1505.07577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-28T07:50:28Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"eef1d879bd3fbc4f91a54d8c1e185ad3640913d5c16cc933af813433656aa77f","abstract_canon_sha256":"10d48601e409a59dd780e09a0987bd898b96a12c917fe3b2f6e559e5db092a51"},"schema_version":"1.0"},"canonical_sha256":"0d11b5ae197e631b4b979f545484ec15d7dd6dbf5b9998cf93c398834aa640ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:28.283634Z","signature_b64":"ovEJNJg2xNtNBqpuzNWURvTPmKb4S6AKRxFF0xe7Kd+CcW+gvNUvIBI14FlU1BRO5tFk+Yd26CDPZC1jSTZQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d11b5ae197e631b4b979f545484ec15d7dd6dbf5b9998cf93c398834aa640ec","last_reissued_at":"2026-05-18T00:41:28.282849Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:28.282849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.07577","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tjTraBcsz9llu40eq5nDH8T/R4hBiovvptEQqLju+FY4JimaCEOmgiqSam2EeQoQAb2gLX6/hxXoSUd3jDfRAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T16:22:45.672440Z"},"content_sha256":"daca80ec87ca98b918f5b7fe06973a805b6f81abf7277f6db43c469c457b5182","schema_version":"1.0","event_id":"sha256:daca80ec87ca98b918f5b7fe06973a805b6f81abf7277f6db43c469c457b5182"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BUI3LLQZPZRRWS4XT5KFJBHMCX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mass formulas for local Galois representations and quotient singularities II: dualities and resolution of singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Melanie Machett Wood, Takehiko Yasuda","submitted_at":"2015-05-28T07:50:28Z","abstract_excerpt":"A total mass is the weighted count of continuous homomorphisms from the absolute Galois group of a local field to a finite group. In the preceding paper, the authors observed that in a particular example, two total masses coming from two different weightings are dual to each other. We discuss the problem how general such a duality holds and relate it to the existence of simultaneous resolution of singularities, using the wild McKay correspondence and the Poincar\\'e duality for stringy invariants. We also exhibit several examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07577","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l8P2Ae3zTW2hM4BpXIbANiatcyT3rHqIBYI0kOr7lqI72t3A6J3CeD60loyen4VUBc8P7CcKiNRDMIZ2+aArAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T16:22:45.672964Z"},"content_sha256":"1b2496d5abce428180517b5706d3aa3b23a572cc0a94f0e0d98d63c957785ecf","schema_version":"1.0","event_id":"sha256:1b2496d5abce428180517b5706d3aa3b23a572cc0a94f0e0d98d63c957785ecf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BUI3LLQZPZRRWS4XT5KFJBHMCX/bundle.json","state_url":"https://pith.science/pith/BUI3LLQZPZRRWS4XT5KFJBHMCX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BUI3LLQZPZRRWS4XT5KFJBHMCX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-24T16:22:45Z","links":{"resolver":"https://pith.science/pith/BUI3LLQZPZRRWS4XT5KFJBHMCX","bundle":"https://pith.science/pith/BUI3LLQZPZRRWS4XT5KFJBHMCX/bundle.json","state":"https://pith.science/pith/BUI3LLQZPZRRWS4XT5KFJBHMCX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BUI3LLQZPZRRWS4XT5KFJBHMCX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BUI3LLQZPZRRWS4XT5KFJBHMCX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"10d48601e409a59dd780e09a0987bd898b96a12c917fe3b2f6e559e5db092a51","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-28T07:50:28Z","title_canon_sha256":"eef1d879bd3fbc4f91a54d8c1e185ad3640913d5c16cc933af813433656aa77f"},"schema_version":"1.0","source":{"id":"1505.07577","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.07577","created_at":"2026-05-18T00:41:28Z"},{"alias_kind":"arxiv_version","alias_value":"1505.07577v1","created_at":"2026-05-18T00:41:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07577","created_at":"2026-05-18T00:41:28Z"},{"alias_kind":"pith_short_12","alias_value":"BUI3LLQZPZRR","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BUI3LLQZPZRRWS4X","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BUI3LLQZ","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:1b2496d5abce428180517b5706d3aa3b23a572cc0a94f0e0d98d63c957785ecf","target":"graph","created_at":"2026-05-18T00:41:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"A total mass is the weighted count of continuous homomorphisms from the absolute Galois group of a local field to a finite group. In the preceding paper, the authors observed that in a particular example, two total masses coming from two different weightings are dual to each other. We discuss the problem how general such a duality holds and relate it to the existence of simultaneous resolution of singularities, using the wild McKay correspondence and the Poincar\\'e duality for stringy invariants. We also exhibit several examples.","authors_text":"Melanie Machett Wood, Takehiko Yasuda","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-28T07:50:28Z","title":"Mass formulas for local Galois representations and quotient singularities II: dualities and resolution of singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07577","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:daca80ec87ca98b918f5b7fe06973a805b6f81abf7277f6db43c469c457b5182","target":"record","created_at":"2026-05-18T00:41:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"10d48601e409a59dd780e09a0987bd898b96a12c917fe3b2f6e559e5db092a51","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-28T07:50:28Z","title_canon_sha256":"eef1d879bd3fbc4f91a54d8c1e185ad3640913d5c16cc933af813433656aa77f"},"schema_version":"1.0","source":{"id":"1505.07577","kind":"arxiv","version":1}},"canonical_sha256":"0d11b5ae197e631b4b979f545484ec15d7dd6dbf5b9998cf93c398834aa640ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d11b5ae197e631b4b979f545484ec15d7dd6dbf5b9998cf93c398834aa640ec","first_computed_at":"2026-05-18T00:41:28.282849Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:28.282849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ovEJNJg2xNtNBqpuzNWURvTPmKb4S6AKRxFF0xe7Kd+CcW+gvNUvIBI14FlU1BRO5tFk+Yd26CDPZC1jSTZQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:28.283634Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.07577","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:daca80ec87ca98b918f5b7fe06973a805b6f81abf7277f6db43c469c457b5182","sha256:1b2496d5abce428180517b5706d3aa3b23a572cc0a94f0e0d98d63c957785ecf"],"state_sha256":"c5ea5aa8d38593e34af8271af7468566b431831b3509f7b526d4800b456557fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IYiRMrVyn9haFBK7F7cvgoktk2uWz18JqSqhlaUjDr6siYZJiTwTlq5G/ptl9RIWoBzE+O1y4oHAgBXyc3M9Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T16:22:45.676618Z","bundle_sha256":"da63274d263e4703e46d162211cc6dbc1819c085582ef827f739162f1791c81e"}}